Course Objectives
Learning purposes : The purpose is to ensure a comprehensive understanding of mathematics learned so far, and to connect that to applied ability in specialized subjects.
Course Objectives :
1. To understand the definition of linear transformation.
2. To understand the synthetic transformation and the inverse transformation.
3. To be able to find a linear transformation that represents the rotation in the plane.
4. To be able to obtain the derivative of the second order or higher.
5. To understand the parameter representation of a function and be able to calculate its derivative.
6. To be able to obtain the area of the figure surrounded by the basic curve.
7. To be able to obtain the lengths of various curves.
8. To be able to obtain the volume of a basic solid.
Rubric
| Excellent | Good | Acceptable | Unacceptable Level |
| Achievement 1 | Understands the properties of elementary functions and can solve applied problems. | Understands the properties of elementary function and can solve about 70% of basic problems. | Understands the properties of elementary functions and can solve about 60% of basic problems. | Cannot understand the nature of elementary functions and cannot solve basic problems. |
| Achievement 2 | Understands linear algebra and can solve applied problems. | Understands linear algebra and can solve about 70% of basic problems. | Understands linear algebra and can solve about 60% of basic problems. | Cannot understand linear algebra and cannot solve basic problems. |
| Achievement 3 | Understands differential calculus and can solve applied problems. | Understands differential calculus and can solve about 70% of basic problems. | Understands differential calculus and can solve about 60% of basic problems. | Cannot understand differential calculus and cannot solve basic problems. |
| Understands the integral method and can solve applied problems. | Understands the integral method and can solve about 70% of basic problems. | Understands the integral method and san solve about 60% of basic problems. | Cannot understand the integral method and cannot solve basic problems. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : Specialized
Field of learning : Mathematics / Physics
Required, Elective, etc.: Elective must complete subjects
Foundational academic disciplines : Mathematical Science / Mathematics / Basic Analysis
Relationship with Educational Objectives : This subject is equivalent to "(3) Acquire deep foundation knowledge of the major subject area".
Relationship with JABEE programs : The main goal of learning / education in this class are "(A) , A-1 "
Course outline: Organize the mathematics that students have learned in a distributed manner, comprehensively relearn the units, such as functions and graphs, calculus, and linear algebra, and establish comprehensive understanding through exercises.
Style:
Course method : In the first half, we will learn the application of matrices. After that, solve the exercises assigned in almost every class. Assignments will be given during summer vacation and winter vacation, and students will submit an assignment report. In the second half, we will learn the application of integration.
Grade evaluation method : 4 regular tests (50%) and reports (50%). Depending on grades, a re-examination may be conducted (additional report assigned) with an upper limit of 80 points on the retest. Textbooks and notebooks are not allowed for the exam.
Notice:
Precautions on enrollment : It is necessary to take this course in order to complete the course for the academic year.
Since this course is intended to acquire comprehensive ability in basic mathematics necessary for engineering, it is a vital step for students.
Foundational subjects : Fundamental Mathematics I (1st year),Fundamental Mathematics Practice (1st), Differential and Integral Ⅰ (2nd), Fundamental Linear Algebra (2nd)
Related subjects : Differential and Integral Ⅱ (3rd year), Fundamental Differential Equations (3rd), Applied Mathematics I, II (4th), Mathematics Continuation (4), Complex Analysis (5th), many other specialized subjects
Attendance advice: If the number of latecomers is large, a warning will be given.
Later, lates may be treated as absent.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Guidance, application of matrix [Linear transformation] |
|
| 2nd |
Application of matrix [Linear transformation 1] |
Understanding Matrix Application [Linear Transformation]
|
| 3rd |
Application of matrix [Linear transformation 2] |
Understanding Matrix Application [Linear Transformation]
|
| 4th |
Application of matrix [eigenvalues and their applications 1] |
Understanding Application of matrix [eigenvalues and their applications]
|
| 5th |
Application of matrix [eigenvalues and their applications 2] |
Understanding Application of matrix [eigenvalues and their applications]
|
| 6th |
Application of matrix [eigenvalues and their applications 3] |
Understanding Application of matrix [eigenvalues and their applications]
|
| 7th |
Comprehensive confirmation of linear algebra |
|
| 8th |
First term midterm exam |
|
| 2nd Quarter |
| 9th |
Return and explanation of answers, comprehensive confirmation of trigonometric functions |
Comprehensive understanding of trigonometric functions
|
| 10th |
Exponential function, logarithmic function |
Comprehensive understanding of exponential and logarithmic functions
|
| 11th |
Quadratic curve |
Comprehensive understanding of quadratic curves
|
| 12th |
Comprehensive confirmation of linear algebra 1 |
Understanding of plane vectors and space vectors
|
| 13th |
Comprehensive confirmation of linear algebra 2 |
Understanding matrices and determinants
|
| 14th |
Comprehensive confirmation of linear algebra 3 |
Understanding eigenvalues and eigenvectors
|
| 15th |
Last term exam |
|
| 16th |
Return and commentary of answers, general exercises |
|
| 2nd Semester |
| 3rd Quarter |
| 1st |
Comprehensive confirmation of differential calculus 1 |
Understanding of differential coefficients
|
| 2nd |
Comprehensive confirmation of differential calculus 2 |
Understanding differential calculus
|
| 3rd |
Comprehensive confirmation of integration method 1 |
Understanding indefinite integrals
|
| 4th |
Comprehensive confirmation of integration method 2 |
Understanding definite integrals
|
| 5th |
Application of differentiation |
Understanding Application of differentiation
|
| 6th |
Application of differentiation / integration [parameter display, polar coordinates, improper integral, etc.] |
Understanding parametric representation, polar coordinates, improper integrals
|
| 7th |
後期中間試験 |
|
| 8th |
Return and commentary of answers, general exercise 1 |
|
| 4th Quarter |
| 9th |
Comprehensive exercise 2 |
|
| 10th |
Comprehensive exercise 3 |
|
| 11th |
Comprehensive exercise 4 |
|
| 12th |
Comprehensive exercise 5 |
|
| 13th |
Comprehensive exercise 6 |
|
| 14th |
Comprehensive exercise 7 |
|
| 15th |
Year-end exam |
|
| 16th |
Return and commentary of answers, general exercise 8 |
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 50 | 0 | 0 | 0 | 0 | 50 | 100 |
| Basic Proficiency | 50 | 0 | 0 | 0 | 0 | 50 | 100 |
| Specialized Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |